Metraipolis › archive › dc_a67b24940fba

On solving integer bilevel optimization problems with a non-convex quadratic follower objective function using disjunctive cuts — arXiv:2610.01197

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01197
License (as archived): CC0-1.0
Archived: 2026-10-06T16:00:39.438Z
SHA-256 of the archived text: e07cca1166437d057688495696237584715712d647ad27809003da34c28d8811
Stable URL of this page: https://metraipolis.com/documento/dc_a67b24940fba

How to cite

On solving integer bilevel optimization problems with a non-convex quadratic follower objective function using disjunctive cuts — arXiv:2610.01197 — arXiv (en), https://arxiv.org/abs/2610.01197 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a67b24940fba (Metraipolis archive dc_a67b24940fba, sha256 e07cca1166437d057688495696237584715712d647ad27809003da34c28d8811)

BibTeX

@misc{dca67b24940fba,
  title = {On solving integer bilevel optimization problems with a non-convex quadratic follower objective function using disjunctive cuts — arXiv:2610.01197},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01197},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a67b24940fba; sha256 e07cca1166437d057688495696237584715712d647ad27809003da34c28d8811},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01197. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this work, we study bilevel optimization problems where all variables are integer, all constraints and the leader objective function are linear, and the follower objective function is non-convex quadratic. Relying on bilevel-free sets derived from improving directions, we develop a disjunctive cut approach to exclude bilevel-infeasible solutions within a branch-and-cut algorithm. We show that our disjunctive cuts can be obtained by solving a cut generating linear program. Furthermore, we discuss conditions that allow the number of disjuncts in the cut generating linear program to be reduced, and we propose several strategies to identify improving directions and generate disjunctive cuts efficiently. We evaluate various aspects of the proposed branch-and-cut algorithm on both convex instances from the literature that fit our setting and new non-convex instances and compare the performance of our best approach with existing state-of-the-art approaches, which we significantly outperform.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Discrete Mathematics (cs.DM).
Pagina del lavoro: https://arxiv.org/abs/2610.01197 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T15:14:57.954Z dalla pagina https://arxiv.org/catchup/math.OC/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).